he twelfth
and all its sub-multiples.

A fundamental note robbed of all its harmonics is hard to obtain, which
is not a matter for regret, as it is a most uninteresting sound. To get
a rich tone we must keep as many useful harmonics as possible, and
therefore a piano hammer is so placed as to strike the string at a point
which does not interfere with the best harmonics, but kills those which
are objectionable. Pianoforte makers have discovered by experiment that
the most pleasing tone is excited when the point against which the
hammer strikes is one-seventh to one-ninth of the length of the wire
from one end.

The nature of the material which does the actual striking is also of
importance. The harder the substance, and the sharper the blow, the more
prominent do the harmonics become; so that the worker has to regulate
carefully both the duration of the blow and the hardness of the hammer
covering.

[26] Tyndall, "On Sound," p. 75.

[27] A Broadwood "grand" is made up of 10,700 separate pieces, and in
its manufacture forty separate trades are concerned.

[28] Twelve notes higher up the scale.

Chapter XV.

WIND INSTRUMENTS.

Longitudinal vibration--Columns of air--Resonance of columns of
air--Length and tone--The open pipe--The overtones of an open
pipe--Where overtones are used--The arrangement of the pipes and
pedals--Separate sound-boards--Varieties of stops--Tuning pipes and
reeds--The bellows--Electric and pneumatic actions--The largest
organ in the world--Human reeds.

LONGITUDINAL VIBRATION.

In stringed instruments we are concerned only with the transverse
vibrations of a string--that is, its movements in a direction at right
angles to the axis of the string. A string can also vibrate
longitudinally--that is, in the direction of its axis--as may be proved
by drawing a piece of resined leather along a violin string. In this
case the harmonics "step up" at the same rate as when the movements were
transverse.

Let us substitute for a wire a stout bar of metal fixed at one end only.
The longitudinal vibrations of this rod contain overtones of a different
ratio. The first harmonic is not an octave, but a twelfth. While a
tensioned string is divided by nodes into two, three, four, five, six,
etc., parts, a rod fixed at one end only is capable of producing only
those harmonics which correspond to division into three, five, seven,
nine, etc., parts. Therefore a free